Plug -8 in wherever there is an m
6(-8) = -8-4[-2(-8)+1-(-8)]
-48 = -8-4(16+1+8)
-48 = -8-4(25)
distribute the -4
-48= -8-100
-48=-108
which means -8 is not the right solution
1.
x = 2
2.
x = 7
3.
x = 7
4.
x = 6
5.
x = 11
6.
x = 11
Answer:
y=4x-4
Step-by-step explanation:
You know that a line perpendicular to the equation (y= -1/4x-14) would have an opposite reciprocal slope.
The slope from the given equation is -1/4x. Take the opposite reciprocal and you get 4/1x or 4x as your slope.
Now use the point-slope formula to find your b value.
(y-y1)=m(x-x1)
m= 4
Plug in (3,8) for x and y, and solve.
(y-8)= 4(x-3)
y-8= 4x -12
y=4x-4
Ratio of tea to lemonade in the new mixture is 3 : 2
<h3><u>Solution:</u></h3>
Given that volume of a beverage prepared by Miki containing tea and lemonade = 2 gallons
Ratio of tea and lemonade in beverage prepared by Miki = 3:1
Then Miki added one half of gallon of lemonade to the mixture.
Need to determine ratio of tea and lemonade in the new mixture.
Lets first calculate volume of tea and volume of lemonade in old mixture that is the one before adding one half of gallon of lemonade.
Given ratio of tea and lemonade in old mixture = 3: 1 , means our of every four parts of mixture, 3 parts are of tea and 1 part is of lemonade.
Given that one-half gallon of lemonade is added to old mixture to form new mixture.
So Volume of lemonade in new mixture = Volume of lemonade in old mixture + one half gallon = 0.5 + 0.5 = 1 gallon
As there is no change in volume of tea , so Volume of Tea in new mixture = Volume of tea in old mixture = 1.5 gallons
Ratio of tea : lemonade in new mixture = 1.5 : 1 = 3 : 2
Hence ratio of tea to lemonade in the new mixture is 3 : 2.
Answer
A) y = x - 7
Step-by-step
Part 1: Convert to slope-intercept form
The equation -x + y = 5 has to be converted from standard form to slope-intercept form before we can begin solving this problem. The slope-intercept form is y = mx + b, where m is the slope of the line and b is its y-intercept. To convert it, just get y by itself on the left side.
-x + y = 5
y - x = 5
y - x + x = 5 + x
y = 5 + x
y = x + 5
This equation tells us the slope of the line (1) and the line's y-intercept (5)
Part 2: Find the equation of the line that is parallel to y = x + 5 and passes through the point (2, -5)
Parallel lines have equal slopes, so the slope of the line we are looking for will be 1 (or just x). So we can rule out answer choice D because it has a slope of -1 (or -x). To find the y-intercept for the line, we need to find the point where x = 0. We can work backwards with the rise over run method to find this point.
m = rise / run = change in y / change in x
1 = 1 / 1
We can use this information to perform a series of transformations (down 1 unit then left 1 unit) that will bring us to the y-intercept.
(2, -5) --> (1, -6)
(1, -6) --> (0, -7)
The point (0, -7) has an x-coordinate of 0, which means that the line intercepts the y-axis at this point.
The slope of the desired line is 1 and its y-intercept is -7.
Part 3: Substitute into the slope-intercept equation
y = mx + b
m = slope = 1 = x
b = y-intercept = -7
y = x - 7